Category: Methodology

A few hours after posting my long post about economic fables yesterday, I saw a tweet by Noah Smith that linked to this long, worthwhile, lecture by DeLong on what it is to "think like an economist". I may post a reaction to it, but first I need to really absorb its message. On a first skimming, it seems a very good one.

I am revamping the introductory graduate microeconomics course for the fall and have added to my recommended summer readings that I emailed my students the book Economic Fables by Ariel Rubinstein. This went to their inboxes a few weeks after other recommended readings that are much more technical and was intended to reinforce what I feel is my most ignored injunction to graduate students, which is to be acutely aware of the limits of economic theories they learn and use. I elaborate here on how I hope this reinforcement can happen.

Rubinstein takes an apparently extreme stance in Economic Fables. He denies that economic theory is useful. He calls economic models “fables”. In the interview that you can find in the book’s link given above, he says that a fable is a fantasy story that, if it is a good one, gives us some insight about the real world. But you cannot use a fable to predict real-world outcomes.

For an economic theorist, like Rubinstein and myself, building fantastical worlds in economic models (or fables) is valuable for the insight it offers on the structure of economic activity, and that is value enough for Rubinstein. Creating and studying economic models needs no further argument to justify its presence in Universities, or the salaries of economic theorists. Further, there is a risk that unscrupulous people may point to economic models, written in a mathematical language that is inscrutable to most, to give the discipline of economics an unwarranted aura of being a true science.

After I sent my email to the incoming graduate students, I worried that they would come to our first class in the end of August a little puzzled by this book recommendation. Why did I ask them to read Economic Fables? Doesn’t it undermine the desire to learn microeconomic theory, the subject of our class? Does it not take time away from studying the other materials I asked them to study over the summer to get readier for the class?

Before I offer my answers to these questions, let me link to a recent piece I enjoyed about the good (useful!) recent developments in economics, by Noah Smith. He points out that criticisms of economics that say it has become a religion, with its dogmatic theories, abound. Doesn’t this fit well with Rubinstein’s use of “fables” for “models”?

It fits well, but it is not an accurate criticism, and it is not productive. Lest it seem that I am lumping Rubinstein in the previous sentence, I hasten to add that I read his book as a deliberate provocation to economists and as a potentially very useful one. It is true that economic models by themselves cannot help us predict anything. They are fantasies. How then did economists find so many applications of some of their models that have clearly worked in the real world? Here is a list of such successes, from Noah Smith’s piece:

First, economists have developed some theories that really work. A good scientific theory makes testable predictions that apply to situations other than those that motivated the creation of the theory. Slowly, econ is building up a repertoire of these gems. One of them is auction theory, which predicts how buyers will bid for things like online ads or spectrum rights — Google’s profits are powered by econ theory as much as by search algorithms. Another example is matching theory, which has made it a lot easier to get an organ transplant. A third is random-utility discrete choice theory, which is used in everything from marketing to transportation planning to disaster preparedness.

Nor are econ’s successful theories limited to microeconomics. Gravity models of trade, though fairly simple in nature, have proven very successful at predicting the flow of international trade.

This list includes, of course, the one success that lets economists claim an economic theory has saved lives directly (via organ transplant chains, made possible by the work of economics Nobel prize winner Alvin Roth and colleagues such as Tayfun Sönmez). Others will surely want to add their favorite successful economic theories.

How did these successes happen? And how did the economics profession turn successfully to empirical work informed by economic fables, as Noah Smith’s article discusses so well?

Answering these questions finally brings me to answer my previous ones. Fables are fantastical stories, yes. Yet, they can be sometimes matched to the infinitely messier world we observe around us, by setting up a correspondence between fable elements and aspects of reality, to allow us to make some good predictions and improve the fables by careful empirical testing. There is a classic paper by a physicist Eugene Wigner about the “unreasonable effectiveness of mathematics in the natural sciences“. Physicists were astonished by the effectiveness of mathematical fables in explaining the natural world around us. Social scientists have a much harder problem than physicists, studying large aggregations of human beings with all their agency and foibles, but they found fables useful too.

What makes the difference? How can a fable be useful in the social sciences, such as economics? It takes the talent of a good social scientist, coupled with hard-earned experience and knowledge of empirical methods, to find correspondences between the elements of a fable and observed social reality. The fables themselves do not provide instruction how to do this.

This is why I asked my students to read Rubinstein’s Economic Fables. I am convinced that you need economic fables, written in the powerful language of mathematics, to start being useful as an applied economist — the program in which I teach is designed to orient graduate students to applied economics in several fields. My colleagues can offer instruction on how to apply the fables better than I can, but I will teach some of the basic fables. I want the students to know just what these fables are for and what the limitations of fables are. This will be more useful for their careers in the long run than just the techniques (hard enough as mastering the techniques will prove in the next few months for my students).

So, dear students, I hope you manage to hold in your mind both the idea that economic models are fables (despite the implication some draw that they are useless because they are fables) and the idea that these fables are essential tools for any economist, but not the only essential tools. As you study, pay close attention to the assumptions in every model you encounter. (One of the best defenses of using mathematics extensively in economics is that it forces researchers to state their assumptions.) Think about how you would connect these assumptions with economic data that you can conceivably obtain. Go back and forth between fables and data. In Econometrics class, think of fables you can use to design your term paper. In Microeconomics (our class) and Macroeconomics, think about how you would subject the fables you are learning to scrutiny when you are finally finished with exams and start doing some independent research. In Mathematics for Economics, motivate yourself to persevere by remembering that you are amassing fable-building tools in a universal language that facilitates clear thinking and pushes back against intellectual dishonesty. Do these things, and your education will be professionally and personally useful and rewarding.

Rajiv Sethi wrote a beautifully clear and succinct account of Thomas Schelling’s contributions to the methodology of economics and to the theory of housing segregation and bargaining. Highly recommended!

In a mostly auto-generated translation via Twitter’s web interface, this says “[we] use mathematics not because we’re smart but because we’re not smart”.

I agree wholeheartedly. Using mathematics in our work in economics (and in so many other areas of research) allows us to stand on the shoulders of giants and use their smarts. It’s on us to make good use of this powerful tool, honed over the centuries by so many brilliant people. Criticisms of using mathematics in economics are pointless; criticisms of using mathematics badly in economics are valuable.

On my train ride to the office this morning, I saw this article by David Sloan Wilson, which is an update of Paul Krugman’s 1996 use of evolutionary biology to improve the methodology of economics. David Sloan Wilson’s post is an update on the developments in theory of evolution since then and their impact on Krugman’s assessment of how economics is, and should be, done. I highly recommend the Wilson article to anyone interested. In addition to being highly informative and well written, it has a good collection of citations worth following up.

The pursuit of beauty and economic theory: friends or enemies?

I read this post on Aeon by Frank Wilczek this morning. I posted about it on Facebook but doing so did not make me stop thinking about it. I want to put some of these thoughts down here, as they relate to economic theory, what draws me to it, and whether the draw of beauty in the mathematics used in economic theory detracts from the theory’s value to society. First of all, I invite you to follow the link above and come back to read the rest of my thoughts.

Wilczek has published a book recently, A Beautiful Question: Finding Nature’s Deep Design (Google Play link, Amazon link). I have not read it to the end yet, but I hope I will over the winter break. His discussion in the Aeon post immediately made me think about the art of mathematics and how it motivates me (and many others) to do economic theory and guides our attempts to do it.

Empires built on math

In my early years studying for my doctorate, I thought of math as a collection of empire-building tools for empires of the mind (castles in the sky might be another apt name). Economic theory, heavily math-laden, becomes in this view a galaxy far, far away where each theorist builds an empire (or at least a few starships) to impose order on the universe. Once you have laid down your assumptions, you then have a solid foundation for building and you are the emperor of your theoretical creations, as long as you can write down your mathematical arguments correctly.

This view is not far from Asimov’s galactic empire fiction. Indeed, Asimov himself thought that some sort of social physics exists, and if we can discover its laws, we could predict the unfolding of societies over vast, even galactic, scales. For economics, this perspective explains at least some of the psychological attraction theorists feel towards their castles in the sky. This attraction is particularly prominent for me when I am working on general equilibrium theory, which most of the profession has left behind.

Ethereal but irrelevant?

Good question! Let me first tell a story about logic and the demise of the Hilbert program in mathematics. Then I will talk about the fragmentation of economic theory, this one brought about by the confrontation of the theory with empirical tests, such as they are (famously much harder in the social sciences than in physics).

Hilbert was a prominent German mathematician. His famous and eponymous program was an attempt to make all mathematics utterly rigorous by putting it on a formal basis and to prove within that framework that mathematics is consistent. (Perhaps the best way to understand “formalization” in this sense, besides the obvious which is that it should be totally understandable to a computer, is by thinking about something von Neumann said: “Young man, in mathematics you don’t understand things. You just get used to them.” —source)

Hilbert’s program came undone when Kurt Gödel came up with his stunning, deep, and worldview shattering (for mathematicians) Incompleteness Theorems. The gist of these theorems is that if you build all of mathematics on a finite list of axioms, then you cannot prove by using this list of axioms all true theorems of mathematics and you cannot prove that the mathematics you have founded on these axioms is consistent (contains no contradictions).

Coming as it did in 1930, this devastating development seems to be a symptom of the fragmentation of European culture, which was soon to produce a horrible war. But what does it have to do with economic theory? Well, it tells us that the theoretical castles are indeed based on air, not stone foundations.

What’s worse, that’s not all that ails theoretical empire-building in economics. While there are plenty of valid criticisms to aim at empirical research in economics, its basic import is that grand, unified economic theories perform badly. This has led to the growth of “behavioral economics”. (Once again, let me point out how silly this name is: isn’t all economics behavioral? — I prefer psychological economics). However mainstream this field has become, it does have a shattering impact on beautiful theory-building that aims at wide applicability.

We contain multitudes and that can be beautiful too!

Well, it was good enough for Walt Whitman. How about we apply it to the entire society, whose functioning is the domain of study of economic theory, broadly conceived? Does the fragmentation I just talked about make further theory development ugly?

Many social scientists have written on this issue. To me, it seems that a fragmented field of theories can still be an object of beauty in the mind of the theorist. Think of it as a kaleidoscope (a word that literally means “a device for showing beauty”). This is how I attempt to keep my motivation up when I am struggling with long, messy arguments trying to prove something in complicated mathematical models of society that invariably leave my head spinning after only a couple of hours of effort.

Another good thing to say about the fragmented collection of models that constitutes modern economic theory is that it has produced some quite literally life-saving innovations (kidney exchanges, which came from a deeply mathematical field of economic theory called mechanism design theory). A good and easily readable account is Al Roth’s recent book Who Gets What — and Why.

Some others to read on related matters

In conclusion, here are some thoughtful works to read carefully that I constantly feel guilty for not having time to read carefully enough.

Daniel Little has a website portal and a blog about what it means to do social theory, even more widely construed than the widest view of economics.

Dani Rodrik has a recently published book in which he “argues that economics can be a powerful tool that improves the world―but only when economists abandon universal theories and focus on getting the context right”, as the book description on Amazon states. Another book I have started — so I really should wrap this post up now and get back to reading, even without having convinced myself that this gigantic post is as well written as possible! Of course it’s not. But I move on anyway. Ars Longa, Vita Brevis. Or, in the original language of Hippocrates, taken from the last link:

Academic journals frequently do not publish papers that did not find an “interesting” effect. This comes under the “publication bias” moniker. This paper in PLOS One shows one specific ill effect this has on our perceptions of what research has shown: the papers that do make it to publication present an overly optimistic view of the effectiveness of psychological treatment of major depressive disorder.

Paul Romer has a new post about “mathiness”, this time in financial economics. Right at the top of the post, he includes two links to blog posts by Tim Johnson about how mathiness was used to obfuscate what the math says in finance, so that official investigations into the latest financial crisis, the one that started in earnest in 2007, would miss something. In Romer’s words, “People in finance used math to hide what they were doing.” The Johnson posts are rich in material from the beginnings of probability theory, incidentally, and surprised me with a connection to Aristotle and how thinking about money as a universal measure showed people the way to apply math to physics; Johnson also connects finance to a notion of justice. Fascinating stuff! I hope to carve some time out to delve in this more deeply.

Another title for this post could be “Why people who talk about general equilibrium theory should always mention the Arrow-Debreu-McKenzie model, without omitting McKenzie”.

Prompted by a post by Joshua Gans, which I saw first on Google+, I recently bought the book Finding Equilibrium, as on the title of this post. The book contains an insightful discussion of the problem of assigning scientific credit in economics, as the book’s subtitle makes clear: Arrow, Debreu, McKenzie and the Problem of Scientific Credit. I finished the book today. It was published by Princeton University Press very recently, in 2014.

The authors continue an old project of the more senior of the two, Weintraub, that dates from the early 1980s. It has to do with why the Arrow-Debreu paper on the existence of general equilibrium gets more airtime in economic theory circles than McKenzie’s paper, even though the latter was submitted to Econometrica and published a bit earlier than the former.

I must disclose here that Lionel McKenzie was a member of my doctoral dissertation committee. I defended my dissertation at the University of Rochester in 1988 to earn my Ph.D. Furthermore, the professor responsible for my applying (and being accepted, I am sure) to the graduate program in economics at Rochester, Emmanuel Drandakis, was the second person to receive a Rochester Ph.D. in economics after McKenzie created the economics department and graduate program there in the late 1950s. Thus, I was immersed in the story of McKenzie’s unfair treatment in not receiving a Nobel Prize, unlike Arrow and Debreu. The story was “in the air” at Rochester, but I did not hear McKenzie himself talk about it, to the best of my recollection. This accords with my memory of McKenzie as a perfect gentleman; in the book I am talking about here, he is described as “classy” by one of the economists quoted there.

I enjoyed the book and read it in a couple of days, even as it came in the middle of a week that started with some worries in my personal life. It gave me the idea of writing a paper about the now ignored general equilibrium approach as it, I think, should be revived in conjunction with extensions to make it properly include collective goods and externalities (an approach that should proceed with techniques not only limited to the axiom-and-proof ones that were the hallmark of the emergence of general equilibrium in the 1950s). I have worked in this area before, myself, so I may have something new of interest to say by revisiting it. However, I did not want to wait to post here until I wrote a paper; that would mean quite a long wait!

Apart from the inclusion of some jargon from the sociology of science and (naturally) from economics, the book is very well written for a general audience. It flows well and is very instructive. The authors make the best of the fact that their topic allows them, by its very nature, to tell it as a story of people and their interactions. Readers always want stories (as we must remember every time we have to teach abstract ideas in the classroom).

As someone who is well versed in general equilibrium theory (although I’ve been neglecting it lately), I found the exposition of the theory’s inception in the book well done. Furthermore, it gave me a few perspectives and some context I did not already have. If I were to teach general equilibrium again, I would be sure to assign parts of this book to complement the rather dry and scary (for students) mathematics that dominate the theory.

Gans’s post that led me to this book concluded that, of the three main protagonists, Debreu emerges in the most unfavorable light. That is indeed my impression and it comes from documentary evidence of his behavior as a referee of McKenzie’s paper for Econometrica and also vis-a-vis his own co-author, Kenneth Arrow, from whom he kept secret his knowledge that McKenzie was already working on his own paper on pretty much the same topic. By contrast, McKenzie emerges clearly as the wronged party and Arrow as quite generous in giving credit to scholars who preceded him.

So, for the very few of you who say “Arrow-Debreu”, please do remember to say “Arrow-Debreu-McKenzie” when talking about general equilibrium theory.

[Edited 2014-09-29 to correct some infelicities in my use of English.]